Description Logics (DLs) are used to represent terminological knowledge, i.e., concepts, objects, and their relationships. Intensive research on DLs during the last fifteen years led to highly optimized systems that allow to reason about DL-knowledge bases. The main feature of such DL-systems are inference services testing consistency of knowledge bases and computing subconcept/superconcept hierarchies. However, as first observed at the AT&T Labs, applications often require additional "non-standard" inferences to support the construction and maintenance of knowledge bases. This book provides a formal foundation of the most prominent non-standard inferences including precise definitions, complete algorithms, and thorough complexity analyses.